Simulating and detecting autocorrelation of molecular evolutionary rates among lineages

Evolutionary timescales can be estimated from genetic data using phylogenetic methods based on the molecular clock. To account for molecular rate variation among lineages, a number of relaxed‐clock models have been developed. Some of these models assume that rates vary among lineages in an autocorrelated manner, so that closely related species share similar rates. In contrast, uncorrelated relaxed clocks allow all of the branch‐specific rates to be drawn from a single distribution, without assuming any correlation between rates along neighbouring branches. There is uncertainty about which of these two classes of relaxed‐clock models are more appropriate for biological data. We present an R package, NELSI, that allows the evolution of DNA sequences to be simulated according to a range of clock models. Using data generated by this package, we assessed the ability of two Bayesian phylogenetic methods to distinguish among different relaxed‐clock models and to quantify rate variation among lineages. The results of our analyses show that rate autocorrelation is typically difficult to detect, even when there is complete taxon sampling. This provides a potential explanation for past failures to detect rate autocorrelation in a range of data sets.     

The likelihood node density effect and consequences for evolutionary studies of molecular rates

Many molecular phylogenies show longer root-to-tip path lengths in species-rich groups, encouraging hypotheses linking cladogenesis with accelerated molecular evolution. However, the pattern can also be caused by an artifact called the node density effect (NDE): this effect occurs when the method used to reconstruct a tree underestimates multiple hits that would have been revealed by extra nodes, leading to longer root-to-tip path lengths in clades with more terminal taxa. Here we use a twofold approach to demonstrate that maximum likelihood and Bayesian methods also suffer from the NDE known to affect parsimony. First, simulations deliberately mismatching the simulation and reconstruction models show that the greater the model disparity, the greater the gap between actual and reconstructed tree lengths, and the greater the NDE. Second, taxon sampling manipulation with empirical data shows that NDE can still be present when using optimized models: across 12 datasets, 70 out of 109 sister path comparisons showed significant evidence of NDE. Unless the model fairly accurately reconstructs the real tree length-and given the complexity of real sequence evolution this may be uncommon -- it will consistently produce a node density artifact. At commonly encountered divergence levels, a 10% underestimation of tree length results in > or = 80% of simulated phylogenies showing a positive NDE. Bayesian trees have a slight but consistently stronger effect. This pervasive methodological artifact increases apparent rate heterogeneity, and can compromise investigations of factors influencing molecular evolutionary rate that use path lengths in topologically asymmetric trees.     

Neutral theory, phylogenies, and the relationship between phenotypic change and evolutionary rates

The neutral theory of molecular evolution predicts that rates of phenotypic change are largely independent from genotypic change. A recent study by Bromham et al. (2002) confirmed this expectation, finding no evidence for correlated phenotypic and molecular evolutionary rates in animals. We reevaluate this hypothesis, sampling at different taxonomic levels in plants and animals, using Bayesian inference to reconstruct phylogenetic trees and estimate rates of molecular evolution. We use independent contrasts in branch lengths to maximize the information extracted from each of the trees and nodal posterior probabilities to assess the influence of phylogenetic error. Our results indicate that in vascular plants between 2% and 11% of the variation in phenotypic rates of change can be explained by the rate of genotypic change. These results may be explained by the idea that processes that affect general evolutionary rates, such as body size, may also be expected to influence rates of morphological change.     

Testing the link between the latitudinal gradient in species richness and rates of molecular evolution

Numerous hypotheses have been proposed to explain latitudinal gradients in species richness, but all are subject to ongoing debate. Here we examine Rohde's (1978, 1992) hypothesis, which proposes that climatic conditions at low latitudes lead to elevated rates of speciation. This hypothesis predicts that rates of molecular evolution should increase towards lower latitudes, but this prediction has never been tested. We discuss potential links between rates of molecular evolution and latitudinal diversity gradients, and present the first test of latitudinal variation in rates of molecular evolution. Using 45 phylogenetically independent, latitudinally separated pairs of bird species and higher taxa, we compare rates of evolution of two mitochondrial genes and DNA-DNA hybridization distances. We find no support for an effect of latitude on rate of molecular evolution. This result casts doubt on the generality of a key component of Rohde's hypothesis linking climate and speciation.     

Time-dependent rates of molecular evolution

For over half a century, it has been known that the rate of morphological evolution appears to vary with the time frame of measurement. Rates of microevolutionary change, measured between successive generations, were found to be far higher than rates of macroevolutionary change inferred from the fossil record. More recently, it has been suggested that rates of molecular evolution are also time dependent, with the estimated rate depending on the timescale of measurement. This followed surprising observations that estimates of mutation rates, obtained in studies of pedigrees and laboratory mutation-accumulation lines, exceeded long-term substitution rates by an order of magnitude or more. Although a range of studies have provided evidence for such a pattern, the hypothesis remains relatively contentious. Furthermore, there is ongoing discussion about the factors that can cause molecular rate estimates to be dependent on time. Here we present an overview of our current understanding of time-dependent rates. We provide a summary of the evidence for time-dependent rates in animals, bacteria and viruses. We review the various biological and methodological factors that can cause rates to be time dependent, including the effects of natural selection, calibration errors, model misspecification and other artefacts. We also describe the challenges in calibrating estimates of molecular rates, particularly on the intermediate timescales that are critical for an accurate characterization of time-dependent rates. This has important consequences for the use of molecular-clock methods to estimate timescales of recent evolutionary events.     

Different rates of substitution may produce different phylogenies of the eutherian mammals

Summary In an attempt to resolve some points of branching order in the phylogeny of the eutherian mammals, a phylogenetic analysis of 26 nuclear and 6 mitochondrial genes was undertaken using a maximum likelihood method on a constant rate stochastic model of molecular evolution. Seventeen of the nuclear genes gave a primates/artiodactyls grouping highest support whereas three of the mitochondrial genes found a rodents/artiodactyls grouping to be best supported. The primates/rodents grouping was never the best supported. On the assumption that rodents are indeed an outgroup to primates and artiodactyls and that the latter taxa diverged 70 million years ago, an estimation was made, for each gene, of the time of divergence of the rodent lineage. In most cases such estimates were beyond the limits set by present interpretations of the paleontological record as were many estimates of the divergence time of mouse and rat. These results suggest that, although there is locus variation, the divergent position of the rodent lineage may be an artifact of an elevated rate of nucleotide substitution in this order.     

Positive correlations between molecular and morphological rates of evolution

The existence of positive associations between rates of molecular and morphological evolution (calculated from branch lengths of phylogenetic trees reconstructed using molecular and morphological characters, respectively) is important to issues of neutrality in sequence evolution, phylogenetic reconstructions assuming neutrality, and evolutionary genotype-phenotype mapping. Rates correlate positively when including branches leading to extant species (tips). Excluding tips, trends are similar, but statistical significances decrease systematically. This is due to (a) lower statistical power (excluding tips reduces sample sizes), and (b) rates are solely calculated from inaccurately reconstructed character states of extinct ancestral species, and this noise decreases correlation strengths. Correlations between molecular and morphological rates of evolution increase as more morphological characters are included for phylogenetic reconstruction. Sequence lengths apparently affect correlations along similar principles. Analyses of plant phylogenies confirm those from animals: sampling biases decrease correlations between molecular and morphological rates of evolution. Results confirm that genotype and phenotype are linked, and suggest adaptive components for molecular evolution. The discussion stresses the difficulties associated with analyses and conclusions based on data deduced from phylogenetic reconstruction.     

Testing the molecular clock: molecular and paleontological estimates of divergence times in the Echinoidea (Echinodermata)

The phylogenetic relationships of 46 echinoids, with representatives from 13 of the 14 ordinal-level clades and about 70% of extant families commonly recognized, have been established from 3 genes (3,226 alignable bases) and 119 morphological characters. Morphological and molecular estimates are similar enough to be considered suboptimal estimates of one another, and the combined data provide a tree that, when calibrated against the fossil record, provides paleontological estimates of divergence times and completeness of their fossil record. The order of branching on the cladogram largely agrees with the stratigraphic order of first occurrences and implies that their fossil record is more than 85% complete at family level and at a resolution of 5-Myr time intervals. Molecular estimates of divergence times derived from applying both molecular clock and relaxed molecular clock models are concordant with estimates based on the fossil record in up to 70% of cases, with most concordant results obtained using Sanderson's semiparametric penalized likelihood method and a logarithmic-penalty function. There are 3 regions of the tree where molecular and fossil estimates of divergence time consistently disagree. Comparison with results obtained when molecular divergence dates are estimated from the combined (morphology + gene) tree suggests that errors in phylogenetic reconstruction explain only one of these. In another region the error most likely lies with the paleontological estimates because taxa in this region are demonstrated to have a very poor fossil record. In the third case, morphological and paleontological evidence is much stronger, and the topology for this part of the molecular tree differs from that derived from the combined data. Here the cause of the mismatch is unclear but could be methodological, arising from marked inequality of molecular rates. Overall, the level of agreement reached between these different data and methodological approaches leads us to believe that careful application of likelihood and Bayesian methods to molecular data provides realistic divergence time estimates in the majority of cases (almost 80% in this specific example), thus providing a remarkably well-calibrated phylogeny of a character-rich clade of ubiquitous marine benthic invertebrates.     

The local-clock permutation test: a simple test to compare rates of molecular evolution on phylogenetic trees

Rates of molecular evolution vary substantially between lineages, and a growing effort is directed at uncovering the causes and consequences of this variation. Comparing local-clocks (rates of molecular evolution estimated from different sets of branches of a phylogenetic tree) is a common tool in this research effort. Here, I show that a commonly used test (the Likelihood Ratio Test, LRT) will not be statistically valid for comparing local-clocks in most cases. Instead, I propose the local-clock permutation test (LCPT), a simple test that can be used to test the significance of differences between local-clocks. The LCPT could also be used to test for differences between any parameter that can be assigned to individual branches on a phylogenetic tree. Using simulated data, I show that the LCPT has good power to detect differences between local-clocks.     

Partitioning the variation in mammalian substitution rates

We have used analysis of variance to partition the variation in synonymous and amino acid substitution rates between three effects (gene, lineage, and a gene-by-lineage interaction) in mammalian nuclear and mitochondrial genes. We find that gene effects are stronger for amino acid substitution rates than for synonymous substitution rates and that lineage effects are stronger for synonymous substitution rates than for amino acid substitution rates. Gene-by-lineage interactions, equivalent to overdispersion corrected for lineage effects, are found in amino acid substitutions but not in synonymous substitutions. The variance in the ratio of amino acid and synonymous substitution rates is dominated by gene effects, but there is also a significant gene-by-lineage interaction.     

Examining rates and patterns of nucleotide substitution in plants

Driven by rapid improvements in affordable computing power and by the even faster accumulation of genomic data, the statistical analysis of molecular sequence data has become an active area of interdisciplinary research. Maximum likelihood methods have become mainstream because of their desirable properties and, more importantly, their potential for providing statistically sound solutions in complex data analysis settings. In this chapter, a review of recent literature focusing on rates and patterns of nucleotide substitution rates in the nuclear, chloroplast, and mitochondrial genomes of plants demonstrates the power and flexibility of these new methods. The emerging picture of the nucleotide substitution process in plants is a complex one. Evolutionary rates are seen to be quite variable, both among genes and among plant lineages. However, there are hints, particularly in the chloroplast, that individual factors can have important effects on many genes simultaneously.     

Purifying Selection Determines the Short-Term Time Dependency of Evolutionary Rates in SARS-CoV-2 and pH1N1 Influenza

High-throughput sequencing enables rapid genome sequencing during infectious disease outbreaks and provides an opportunity to quantify the evolutionary dynamics of pathogens in near real-time. One difficulty of undertaking evolutionary analyses over short timescales is the dependency of the inferred evolutionary parameters on the timespan of observation. Crucially, there are an increasing number of molecular clock analyses using external evolutionary rate priors to infer evolutionary parameters. However, it is not clear which rate prior is appropriate for a given time window of observation due to the time-dependent nature of evolutionary rate estimates. Here, we characterize the molecular evolutionary dynamics of SARS-CoV-2 and 2009 pandemic H1N1 (pH1N1) influenza during the first 12 months of their respective pandemics. We use Bayesian phylogenetic methods to estimate the dates of emergence, evolutionary rates, and growth rates of SARS-CoV-2 and pH1N1 over time and investigate how varying sampling window and data set sizes affect the accuracy of parameter estimation. We further use a generalized McDonald–Kreitman test to estimate the number of segregating nonneutral sites over time. We find that the inferred evolutionary parameters for both pandemics are time dependent, and that the inferred rates of SARS-CoV-2 and pH1N1 decline by ∼50% and ∼100%, respectively, over the course of 1 year. After at least 4 months since the start of sequence sampling, inferred growth rates and emergence dates remain relatively stable and can be inferred reliably using a logistic growth coalescent model. We show that the time dependency of the mean substitution rate is due to elevated substitution rates at terminal branches which are 2–4 times higher than those of internal branches for both viruses. The elevated rate at terminal branches is strongly correlated with an increasing number of segregating nonneutral sites, demonstrating the role of purifying selection in generating the time dependency of evolutionary parameters during pandemics.     

The genome as a life-history character: why rate of molecular evolution varies between mammal species

DNA sequences evolve at different rates in different species. This rate variation has been most closely examined in mammals, revealing a large number of characteristics that can shape the rate of molecular evolution. Many of these traits are part of the mammalian life-history continuum: species with small body size, rapid generation turnover, high fecundity and short lifespans tend to have faster rates of molecular evolution. In addition, rate of molecular evolution in mammals might be influenced by behaviour (such as mating system), ecological factors (such as range restriction) and evolutionary history (such as diversification rate). I discuss the evidence for these patterns of rate variation, and the possible explanations of these correlations. I also consider the impact of these systematic patterns of rate variation on the reliability of the molecular date estimates that have been used to suggest a Cretaceous radiation of modern mammals, before the final extinction of the dinosaurs.     

Stochastic models of molecular evolution and the estimation of phylogeny and rates of nucleotide substitution in the hominoid primates

We have estimated phylogenetic patterns and rates of nucleotide substitution in the hominoid primates using two different probabilistic models of molecular evolution as applied to three different data sets of nucleic acid sequences. The orang-utan was found to be the out-group of the other hominoids examined. Within the African apes and human clade the sister-group relationship of chimpanzee and human was found to be statistically the best, although the magnitude of the error estimates (a reflection of random statistical fluctuations) makes this conclusion tentative. The ψν-globin data sets were found to be statistically the most consistent and gave estimates of the times of divergence of chimpanzee and human from gorilla and of chimpanzee from human as 7·7 ± 1·5 Ma (Millions of years ago) and 7·4 ± 1·5 Ma respectively, although the speculative nature of these estimates is emphasized. In all cases the calibration point was the assumed divergence of the orang-utan from the remaining hominoids at 14·5 Ma. There was no statistically significant evidence of a slowdown in nucleotide substitution rate for the human lineage, or among the hominoids as a whole with respect to the Old and New World monkeys. We advocate the continued use and development of stochastic models of molecular evolution as a basis for phylogenetic estimation. On this basis one can choose between competing hypotheses of relationship in a statistical manner and can provide estimates of the errors involved in such estimations. The assumptions of all stochastic models are open to test and future refinement.     

Rates of molecular evolution in bacteria are relatively constant despite spore dormancy

Rates of molecular evolution are known to vary considerably among lineages, partially due to differences in life-history traits such as generation time. The generation-time effect has been well documented in some eukaryotes, but its prevalence in prokaryotes is unknown. "Because many species of Firmicute bacteria spend long periods of time as metabolically dormant spores, which could result in fewer DNA substitutions per unit time, they present an excellent system for testing predictions of the molecular clock hypothesis." To test whether spore-forming bacteria evolve more slowly than their non-spore-forming relatives, I used phylogenetic methods to determine if there were differences in rates of amino acid substitution between spore-forming and non-spore-forming lineages of Firmicute bacteria. Although rates of evolution do vary among lineages, I find no evidence for an effect of spore-formation on evolutionary rate and, furthermore, evolutionary rates are similar to those calculated for enteric bacteria. These results support the notion that variation in generation time does not affect evolutionary rates in bacterial lineages.     

Relative rates of evolution in the coding and control regions of African mtDNAs

Reduced median networks of African haplogroup L mitochondrial DNA (mtDNA) sequences were analyzed to determine the pattern of substitutions in both the noncoding control and coding regions. In particular, we attempted to determine the causes of the previously reported (Howell et al. 2004) violation of the molecular clock during the evolution of these sequences. In the coding region, there was a significantly higher rate of substitution at synonymous sites than at nonsynonymous sites as well as in the tRNA and rRNA genes. This is further evidence for the operation of purifying selection during human mtDNA evolution. For most sites in the control region, the relative rate of substitution was similar to the rate of neutral evolution (assumed to be most closely approximated by the substitution rate at 4-fold degenerate sites). However, there are a number of mutational hot spots in the control region, approximately 3% of the total sites, that have a rate of substitution greater than the neutral rate, at some sites by more than an order of magnitude. It is possible either that these sites are evolving under conditions of positive selection or that the substitution rate at some sites in the control region is strongly dependent upon sequence context. Finally, we obtained preliminary evidence for "nonideal" evolution in the control region, including haplogroup-specific substitution patterns and a decoupling between relative rates of substitution in the control and coding regions.     

Sequence diversity and rates of molecular evolution between sheep and cattle genes

Experiments that aim to identify genes of importance in sheep are currently inhibited by a paucity of genomic resources. One approach, therefore, is to exploit the wealth of data and associated capabilities becoming available for the bovine genome. Cross-species application of microarrays and comparative sequencing to identify single nucleotide polymorphisms are two possibilities; however, both are dependant on the level of nucleotide sequence similarity between the two species. This study used 120 gene orthologues consisting of over 60 kb of aligned sequence to estimate the gene diversity between cattle and sheep. Less than 3% of protein-coding nucleotide positions were found to be different, indicating that the prospect for successfully using cross-species strategies is high. Substitution at synonymous sites ranged between 6.9 and 7.7% (+/- 0.3%), and was higher than at non-synonymous sites (1.4-1.7 +/- 0.1%). The relative rate test was used to determine whether the observed mutation rates were constant between the two lineages. While the rate at synonymous sites appeared constant, the rate at non-synonymous sites was significantly higher within the caprinae lineage (sheep) when compared with bovinae (cattle; chi2 = 10.03; d.f. = 1, P < 0.01). This is the first demonstration that variable rates of molecular evolution may be present within the family Bovidae.     

Sociality and the rate of molecular evolution

The molecular clock does not tick at a uniform rate in all taxa but may be influenced by species characteristics. Eusocial species (those with reproductive division of labor) have been predicted to have faster rates of molecular evolution than their nonsocial relatives because of greatly reduced effective population size; if most individuals in a population are nonreproductive and only one or few queens produce all the offspring, then eusocial animals could have much lower effective population sizes than their solitary relatives, which should increase the rate of substitution of "nearly neutral" mutations. An earlier study reported faster rates in eusocial honeybees and vespid wasps but failed to correct for phylogenetic nonindependence or to distinguish between potential causes of rate variation. Because sociality has evolved independently in many different lineages, it is possible to conduct a more wide-ranging study to test the generality of the relationship. We have conducted a comparative analysis of 25 phylogenetically independent pairs of social lineages and their nonsocial relatives, including bees, wasps, ants, termites, shrimps, and mole rats, using a range of available DNA sequences (mitochondrial and nuclear DNA coding for proteins and RNAs, and nontranslated sequences). By including a wide range of social taxa, we were able to test whether there is a general influence of sociality on rates of molecular evolution and to test specific predictions of the hypothesis: (1) that social species have faster rates because they have reduced effective population sizes; (2) that mitochondrial genes would show a greater effect of sociality than nuclear genes; and (3) that rates of molecular evolution should be correlated with the degree of sociality. We find no consistent pattern in rates of molecular evolution between social and nonsocial lineages and no evidence that mitochondrial genes show faster rates in social taxa. However, we show that the most highly eusocial Hymenoptera do have faster rates than their nonsocial relatives. We also find that social parasites (that utilize the workers from related species to produce their own offspring) have faster rates than their social relatives, which is consistent with an effect of lower effective population size on rate of molecular evolution. Our results illustrate the importance of allowing for phylogenetic nonindependence when conducting investigations of determinants of variation in rate of molecular evolution.     

Body mass and temperature influence rates of mitochondrial DNA evolution in North American cyprinid fish

The mass-specific metabolic rate hypothesis of Gillooly and others predicts that DNA mutation and substitution rates are a function of body mass and temperature. We tested this hypothesis with sequence divergences estimated from mtDNA cytochrome b sequences of 54 taxa of cyprinid fish. Branch lengths estimated from a likelihood tree were compared with metabolic rates calculated from body mass and environmental temperatures experienced by those taxa. The problem of unknown age estimates of lineage splitting was avoided by comparing estimated amounts of metabolic activity along phyletic lines leading to pairs of modern taxa from their most recent common ancestor with sequence divergences along those same pairs of phyletic lines. There were significantly more pairs for which the phyletic line with greater genetic change also had the higher metabolic activity, when compared to the prediction of a hypothesis that body mass and temperature are not related to substitution rate.